Aatu Koskensilta wrote:> Shmuel (Seymour J.) Metz <spamtrap@library.lspace.org.invalid> writes:>>> There are proposition such that neither P nor ¬P is a theorem, and>> similary there are propositions such that models exist in which P is>> true and other models in which ¬P is true.>> Your wording here perplexing -- "similarly"? -- since it is a> mathematical theorem that P is undecidable in a theory T iff there is a> model of T in which P is false and a model of T in which it is false.>> As a general doctrince, the idea that P is neither true nor false if P> is independent of ZFC is merely silly. Surely you don't mean to suggest> that for instance "ZFC is inconsistent" is neither true nor false?

You seemed to have switched from a technical sense of true (true in a model) to an informal one. Whether that is a silly attempt at trickery on your behalf or a manifestation of your ignorance is hard to tell. So what are you: devious or dim?